1. Field of the Invention
This disclosure relates in general to data channels, and more particularly to a method and apparatus for data coding for high density recording channels exhibiting low frequency contents.
2. Description of Related Art
When data are digitally recorded on, or read-back from, a recording medium, it is preferable that the data are recorded at a high density Because of the enormous increase in demand for data storage capacity, research on general recording systems has resulted in the investigation of many potential methods and architectures for increasing the capacity of storage media. This is also true for magnetic recording, for example in magnetic disk drive data storage systems in which architectures that may result in a higher areal density are being explored.
Recording systems typically employ Run-Length-Limited (RLL) codes to improve the write ability of the recording system and enhance read-back performance. In Non-Return-To-Zero-Inverted (NRZI) format where one denotes transition and zero no transition, RLL codes may be represented by (d, k) constraints, where d and k represent the minimum and maximum number of consecutive zeros between two adjacent ones respectively.
For an encoder encodes m information bits into n coded bits, the code rate is defined as ratio of m over n. The d constraint imposes the minimum separation between two adjacent transitions, while the k constraint helps gain and timing recovery loops in the readback process. The drawback of the d constraint is low code rate efficiency, which is not desirable for high-density recording channels equalized to partial response (PR) shapes.
As an alternative to imposing a constraint on the minimum separation between two adjacent transitions, one can relax this constraint and only limit the maximum number of consecutive transitions called the j constraint in sequence. The resultant codes are called MTR codes, which have much higher code rate efficiency than RLL codes with non-zero d. For example, the capacity of (1, k,) RLL code (in the limit with large k) is 0.6942, however the capacity of (0, k) MTR code with j=3 is 0.8791.
The error rate performance of recording systems equalized to PR shapes is largely dependent on their error events with minimum and near minimum squared distances, where an error event is defined as the difference sequence between two legal sequences in Non-Return-To-Zero (NRZ) format where 1 represents high amplitude, and 0 or −1 represents low amplitude, and the squared distance is defined as the sum of the square of an error event. For example, if the sequence of {1 −1 1} is mistakenly detected as {−1 1 1}, then the resultant error event is denoted as {+−+}, and the squared distance is 12. Some typical error events with small squared distances are {+}, {+−}, {+−+}, {+−+−}, {+0+}, {+00+}, and {+000+}, and their inverse correspondences.
The error event is denoted as the sequence that is obtained by periodically repeating the sequence s, e.g., {xy}=xyxy. In order to improve error rate performance, modern recording channels utilize parity code (also called parity mode) or Viterbi detector metrics of extended targets (also called parity-less mode) to detect certain small distance error events and make corrections on those error events. For example, in parity mode, 1-bit of even parity check may be applied to each codeword.
A channel detector may detect and therefore correct error events with odd weights in each codeword as error events with odd weights violate even parity check condition. In principle, parity mode or parity-less mode can detect certain types of error events and make right corrections on the detected error events with some small miscorrection probabilities. However at high density recording, error events with minimum and near minimum squared distances become clouded, regular error event correction may not be effective as it fails to make clear separations among possible error events with small distances.
Parity mode or parity-less mode processor makes mis-corrections under those conditions that affect error rates after error-correction coding (ECC). MTR code on the other hand limits the maximum run of consecutive transitions to j. As a result, it eliminates many small distance error events which otherwise would occur at high-density recording. For example, MTR code with j=3 eliminates all four or more consecutive transitions. As a result, the error events with alternating signs {+−+− . . . } will be prevented from occurring.
The error rate performance of recording channels can be improved by combining both properties of MTR constraint and parity checking. For example, the MTR j=3 code with 2-bit parity checking eliminates {+−+− . . . } error events and corrects {+}, {+−}, {−+}, and {+00+} error events. To further improve code efficiency, the j-constraint in MTR code can be relaxed to allow j+1 consecutive transitions to occur at certain pre-defined positions as long as those positions are separated by at least 1 bit interval.
This new class of MTR codes is called TMTR codes. For example, TMTR codes with j=3 allows j consecutive transitions to occur at odd positions, and j+1 consecutive transitions to occur at even positions. The TMTR codes with j=3 also eliminate {+−+− . . . } error events, but have much higher code efficiency. For example the TMTR codes with j=3 have capacity of 0.9163, which is 0.0372 higher than MTR codes with j=3. TMTR codes with parity checking have been found superior in performance than non-MTR coded channels with parity in both longitudinal and perpendicular recording systems under certain heads/disk combinations and operational conditions.
Recording channels such as longitudinal recording do not exhibit low frequency contents. These types of recording channels are called DC-free recording channels. The targets of channel detectors are also chosen to be DC-free to match the characteristics of recording channels. On the other hand, some recording channels such as perpendicular recording exhibit low frequency contents.
In longitudinal recording, the magnetic medium on the disc is magnetized parallel to the surface of the disc. In perpendicular recording, however, the medium is magnetized perpendicular to the surface of the disc. According to perpendicular magnetic recording, a recording (write) magnetic field generated from a main pole of the head forms a magnetic path in which the magnetic field is induced to the underlayer disposed on the rear of the recording magnetic layer and returned from an auxiliary pole to the recording head. By switching the direction of the recording magnetic field, the recording magnetic layer is magnetized in two directions towards the thickness of the medium in correspondence with the recording information code, thereby storing information. In such recording, an intensive and steep perpendicular recording (write) magnetic field can be applied to the recording magnetic layer, so that high-resolution information storage can be achieved. Moreover, when magnetized recording information is reproduced from the perpendicular magnetic recording medium recording the information, as described above, by the high-sensitive MR reproducing head using the MR device, a reproduced signal from the head has a rectangular-shaped signal waveform corresponding to the magnetized recording pattern which is sensed immediately by the head.
In addition to its potential to achieve higher areal densities, the specific nature of perpendicular recording also brings its own difficulties. The targets of a channel detector may be chosen to have low-frequency contents to better match the nature of the recording systems. The targets of a channel detector may be categorized into three groups, DC-free targets, DC-full targets, and DC-attenuated targets. The DC-full targets are the ones that exhibit full DC-response or full low frequency energy matching recording systems, while DC-attenuated targets exhibit some low frequency energy which lie in between DC-full targets and DC-free targets in terms of low frequency contents.
If the noise presented to the signal is white, then DC-full targets will be the best choice since they best match the recording channel responses. However if noise is not white, then DC-full targets may not be the best choice in terms of minimum mean square errors (MMSE). For example, the media noise present in modern recording systems is low frequency noise whose spectral shape is similar to channel responses.
With noise pronounced at low frequencies, DC-attenuated targets may become the better choice in balancing signal energy and noise power at low frequencies. The DC-attenuated targets approach DC-free targets when increasingly suppressing DC and low frequency contents. DC-free targets sharply suppress low frequency noise, but also totally eliminate signal energy at DC and heavily suppress signal energy at low frequencies, resulting in losses in signal-to-noise ratio (SNR). For encoded recording systems exhibiting low frequency contents, DC-attenuated targets become favorable choice for improving SNR.
Even though channel detector targets can be DC-full or DC-attenuated, in practice there are AC coupling filters in recording systems and signals entering the read-paths of recording channels are AC coupled. The impact of AC coupling is the removal of low frequency contents in read-back signals, causing signals entering channel detectors to have perturbations at baselines, a phenomenon called baseline wander. Baseline wonder has an adverse impact on channel error rate performance.
One way to compensate for the baseline wander is to apply DC-compensation loops into channels to restore low frequency contents into incoming signals. The effectiveness of DC-compensation is dependent on the high-pass pole frequencies in AC-coupling networks. The higher the high-pass pole frequencies, the harder for DC-compensation loops to work effectively. DC-compensation loop works just like a decision-feedback equalizer (DEF) system, which may be sensitive to error propagation.
The different approach to solving baseline wonder from AC-coupling network for DC-attenuated targets is to apply DC-free or RDS codes to data sequences so that read-back signals from recording channels have much attenuated low frequency components and AC-coupling network will have no or much less impact on read-back signal entering channel equalizer and detector. In digital recording, the spectral null constraints of most importance have been those that prescribe a spectral null at or DC. The sequences are said to be DC-free or charge-constrained. The concept of running digital sum (RDS) of a sequence plays a significant role in the description and analysis of DC-free sequences. For a bipolar sequence ω=ω0, ω1, . . . ωL−1, the RDS of a subsequence ω□, . . . ω□′, denoted RDS(ω□, . . . ω□′) is defined as
      RDS    ⁡          (                        ω          •                ,                  …          ⁢                                          ⁢                      ω            •            ′                              )        =            ∑              i        =        l                    l        ′              ⁢                  ω        i            .      Thus, the spectral density of the sequences vanishes if and only if the RDS values for all sequences are bounded in magnitude by some constant integer.
With the aid of DC-free codes, the DC-compensation loops can be eliminated and channel detector targets can still be selected to include low-frequency energy to better match recording system responses. The main advantage of using RDS codes is that DC-full or DC-attenuated targets can be applied without the need of DC-compensation loops.
DC-full or DC-attenuated targets may produce better error rate performance than DC-free targets under normal operational conditions, but are vulnerable to any low frequency distortions or disturbances that may appear under special conditions. One example is the existence of thermal asperity (TA) disturbance that today's magnetic recording systems experience. TA is a low frequency distortion, which has catastrophic impact on channel detectors that respond to low frequencies.
To eliminate the sensitivity of channel detectors to low frequency disturbances and also minimize the losses in SNR of detectors under normal conditions, RDS codes are used in connection with DC-free targets. DC-free targets suppress low frequency noise and also signal energy at low frequencies. But since signals at low frequencies have little energy due to the RDS constraint, DC-free targets may improve spectral SNR at low frequencies. The improvement of spectral SNR at low frequencies can be achieved by matching the spectrum of RDS codes to that of DC-free targets at low frequencies.
In practical uses in magnetic recording, code rates of RLL codes are preferred to be high in order to achieve good overall error rate performances. The RDS codes are also preferred to have high code rate efficiency for being used in magnetic recording channels. The higher the code rates, the less attenuations of energy at low frequencies, even though energy at DC approaches to zero. In order to match the spectrum of high code rate codes at low frequencies, DC-free targets need to be longer than conventional DC-free targets so that more boosts at low frequencies can be realized. One way to implement long DC-free targets is through post-processing.
As have been seen above, both properties of RDS and MTR constraints are desirable for recording channels exhibiting low frequency contents. However RDS codes do not impose any constraint on j-constraint of data sequences. The RDS coded sequences may have long strings of consecutive transitions. On the other hand, MTR or TMTR codes do not impose any constraint on RDS values of data sequences, and may result in un-bounded RDS values.
Known coding solutions use either MTR/TMTR codes or RDS codes separately. However, the advantages of MTR/TMTR codes and the advantages of RDS codes cannot be realized at the same time due to the fact that the MTR/TMTR codes and RDS codes are different codes.
It can be seen then that there is a need for a method and apparatus for performing data coding for high-density recording channels exhibiting low frequency contents that takes advantage of both RDS and MTR or TMTR constraints.